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Formulas for 2D Solids
Perimeter
Rectangle: P = 2l + 2w
l = Length
w = Width
Square: P = 4s
s = Side length
Triangle: P = a + b + c
a, b, c = Lengths of the three sides
Circle (Circumference): C = 2πr or C = πd
r = Radius
d = Diameter
π (pi) ≈ 3.14159
Trapezoid: P = a + b + c + d
a, b = Lengths of the parallel sides
c, d = Lengths of the non-parallel sides
Area
Rectangle: A = l × w
l = Length
w = Width
Square: A = s²
s = Side length
Triangle:
A = 1/2 * b * h
b = Base
h = Height
A = √(s(s-a)(s-b)(s-c)) (Heron's Formula)
s = Semi-perimeter (s = (a + b + c) / 2)
a, b, c = Sides of the triangle
Area = 1/2 * a * b * sin(C)
a and b are the lengths of two sides of the triangle.
C is the angle between sides a and b.
Circle: A = πr²
r = Radius
π (pi) ≈ 3.14159
Trapezoid: A = 1/2 * h * (a + b)
h = Height (perpendicular distance between the parallel sides)
a, b = Lengths of the parallel sides
Parallelogram: A = b * h
b = Base
h = Height (perpendicular distance between the base and the opposite side)
Rhombus: A = 1/2 * d1 * d2
d1, d2 = Lengths of the diagonals
Formulas for 3D Solids
Surface Area
Cube:
Surface Area = 6a²
a = Side length
Cuboid (Rectangular Prism):
Surface Area = 2(lw + lh + wh)
l = Length
w = Width
h = Height
Sphere:
Surface Area = 4πr²
r = Radius
π (pi) ≈ 3.14159
Cylinder:
Surface Area = 2πrh + 2πr²
r = Radius
h = Height
π (pi) ≈ 3.14159
Cone:
Surface Area = πr(r + l)
r = Radius
l = Slant height
π (pi) ≈ 3.14159
Pyramid:
Surface Area = B + (1/2)pl
B = Area of the base
p = Perimeter of the base
l = Slant height
Prism:
Surface Area = 2B + Ph
B = Area of the base
P = Perimeter of the base
h = Height
Volume
Cube:
Volume = a³
a = Side length
Cuboid (Rectangular Prism):
Volume = l × w × h
Sphere:
Volume = (4/3)πr³
Cylinder:
Volume = πr²h
Cone:
Volume = (1/3)πr²h
Pyramid:
Volume = (1/3) * B * h
B = Area of the base
h = Height